A general optimal inequality for arbitrary Riemannian submanifolds.
Chen, Bang-Yen (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Chen, Bang-Yen (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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A Riemannian manifold is said to be semisymmetric if . A submanifold of Euclidean space which satisfies is called semiparallel. It is known that semiparallel submanifolds are intrinsically semisymmetric. But can every semisymmetric manifold be immersed isometrically as a semiparallel submanifold? This problem has been solved up to now only for the dimension 2, when the answer is affirmative for the positive Gaussian curvature. Among semisymmetric manifolds a special role is played...
Arslan, Kadri, Ezentas, Ridvan, Mihai, Ion, Murathan, Cengizhan, Özgür, Cihan (2002)
International Journal of Mathematics and Mathematical Sciences
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Some examples of slant submanifolds of almost product Riemannian manifolds are presented. The existence of a useful orthonormal basis in proper slant submanifolds of a Riemannian product manifold is proved. The sectional curvature, the Ricci curvature and the scalar curvature of submanifolds of locally product manifolds of almost constant curvature are obtained. Chen-Ricci inequalities involving the Ricci tensor and the squared mean curvature for submanifolds of locally product manifolds...
Kim, Jeong-Sik, Choi, Jaedong (2003)
International Journal of Mathematics and Mathematical Sciences
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Rizza, Giovanni Battista (2003)
Balkan Journal of Geometry and its Applications (BJGA)
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